Calculation of the vibrational partition function of diatomic molecules from a scaled Wigner-Kirkwood expansion

New approximations to the partition function of diatomic molecules are give n. The semiclassical Wigner-Kirkwood expansion truncated at the second or f ourth order diverges as T --> infinity. Various methods of scaling the Wign er-Kirkwood expansion are given which avoid this disadvantage and give suff icient accuracy in the low-temperature region. In addition, two modificatio ns of the Pitzer-Gwinn method are discussed. Most molecular potentials can be considered almost harmonic near the minimum. For the scaling of the Wign er-Kirkwood expansion, therefore, a functional form is chosen, which would be exact for every temperature in the case of a purely harmonic potential. In the high-temperature limit the scaled and the conventional Wigner-Kirkwo od expansion become identical.